Steiner P-algebras
General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them. It has lots of applications in theoretical computer science, secure communications etc. Combinatorial designs play significa...
Збережено в:
Дата: | 2005 |
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Автор: | |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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Назва видання: | Algebra and Discrete Mathematics |
Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156624 |
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Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
Цитувати: | Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of UkraineРезюме: | General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them.
It has lots of applications in theoretical computer science, secure
communications etc. Combinatorial designs play significant role
in these areas. Steiner Triple Systems (STS) which are particular
case of Balanced Incomplete Block Designs (BIBD) from combinatorics can be regarded as algebraic systems. Steiner quasigroups
(Squags) and Steiner loops (Sloops) are two well known algebraic
systems which are connected to STS. There is a one-to-one correspondence between STS and finite Squags and finite Sloops. A new
algebraic system w.r.to a ternary operation P based on a Steiner
Triple System introduced in [3].
In this paper the abstraction and the generalization of the properties of the ternary operation defined in [3] has been made. A new
class of algebraic systems Steiner P-algebras has been introduced.
The one-to-one correspondence between STS on a linearly ordered
set and finite Steiner P-algebras has been established. Some identities have been proved. |
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